Reproducible Global Sums

Reproducible global sums are more expensive and potentially unaffordable for production running. However, they can be useful for debugging purposes so that different processor decompositions don't change the answer.

This can be implemented by adding a new builtin for the reproducible global sums, and simply copying the UM version.
Ben Shipway has started to add a PSyclone builtin to his local copy. It looks like this ...
The generated code looks OK!

class DynXKahanproductYKern(DynBuiltIn):
''' Calculates the inner product of two fields, using Kahan's method
to retain precision in the sum
innprod = SUM( X(:)*Y(:) ) '''

def __str__(self):
    return "Built-in: X_kahanproduct_Y"

def gen_code(self, parent):
    '''
    Generates Dynamo0.3 API specific PSy code for a call to the
    X_kahanproduct_Y Built-in.

    :param parent: Node in f2pygen tree to which to add call
    :type parent: :py:class:`psyclone.f2pygen.BaseGen`
    '''
    from psyclone.f2pygen import AssignGen, DeclGen
    # We sum the DoF-wise product of the supplied fields. The variable
    # holding the sum is initialised to zero in the psy layer.
    # This uses Kahan's method which requires additional local
    # variables
    parent.add(DeclGen(parent, datatype="real", kind="r_def",
                       entity_decls=["local_sum", "corr"],
                       initial_values=["0.0_r_def", "0.0_r_def"]))
    parent.add(DeclGen(parent, datatype="real", kind="r_def",
                       entity_decls=["new_sum", "corr_next"]))
    innprod_name = self._reduction_ref(self._arguments.args[0].name)
    field_name1 = self.array_ref(self._arguments.args[1].proxy_name)
    field_name2 = self.array_ref(self._arguments.args[2].proxy_name)
    # Kahan's method
    rhs_expr =  "corr +" + field_name1 + "*" + field_name2
    parent.add(AssignGen(parent, lhs="corr_next", rhs=rhs_expr))
    parent.add(AssignGen(parent, lhs="new_sum", rhs="local_sum + corr"))
    parent.add(AssignGen(parent, lhs="corr", rhs="corr_next - (new_sum - local_sum)"))
    parent.add(AssignGen(parent, lhs="local_sum", rhs="new_sum"))
    rhs_expr = "local_sum + corr"
    parent.parent.add(AssignGen(parent.parent, lhs=innprod_name, rhs=rhs_expr))